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Puzzle Story - A Grain of Grain


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#61 Cubbie Blues

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Posted 17 January 2013 - 11:22 AM

Was each peasant to give a different amount of bags (we already know that they were not to all give the same)? example of number of bags 2 4 3 8 5 5 9 10 13 12 18 ... in this example two people would have given 5 and the rest were different amounts.

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#62 hansman1982

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Posted 17 January 2013 - 12:00 PM

Yes, although if you have two peasants giving 5 bags a piece how would the Lord be guaranteed to pick the right peasant?

And you now have enough info to piece this thing together.

#63 SirCub

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Posted 17 January 2013 - 04:32 PM

Here's my hypothetical of how the Lord solved it. Assuming there are 20 peasants, each giving a different number of bags, the Lord should know his expected total. For simplicity sake, let's say that each bag weighs 10 pounds and that the number of bags that each peasant are supposed to bring are 1-20, respectively (ie- first peasant brings one bag, second brings two, etc.).

So the total expected weight would be:

sum((1:20)*10) = 2100 lb

Also, since the Lord knows how much he'd be shorted by the water trick, we will assume that the water trick cuts down on the amount of grain in the bag, by 10% of the grain. Thus, the weight of grain that the lord would be shorted in a given bag comes out to:

0.1 * 10 lb = 1 lb/bag

Now, let's assume that the Lord knows all of the above information, and all the peasants come and drop off their bags, and the total weight comes out to 2083 lb, instead of 2100 lb. He could then conclude that he was shorted by:

2100 lb - 2083 lb = 17 lb.

And assuming that the guilty party (assuming there was only one) used the water trick, he would know that they had a a certain number of bags:

17 lb / 1 lb./bag = 17 bags.

Theretofor, I conclude that it was the 17th peasant, the one with 17 bags of grain! The one-armed peasant, your honor! He's the one you want!

#64 SirCub

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Posted 17 January 2013 - 04:33 PM

(if not, I give up)

#65 hansman1982

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Posted 17 January 2013 - 05:44 PM

Yes but why did the one armed peasant shoot the other guy ;).

Excellent work!

#66 lapdawg

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Posted 20 January 2013 - 10:40 AM

Unfortunately, the lord wasn't as smart as he thought he was. If the guilty peasant only water some of the bags, the lord sent the wrong peasant to the dungeon.




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